Properties of a truncated sphere with a power law density profile Suppose the mass distribution of...
Assume that a Spherical Planet Of Radius R, Has a Uniform Mass Density (Per Unit Volume) Distribution Throughout, Of Value Po. Also, Assume that There Is a Massive Dust Cloud In the Rest Of the Universe, Which Decays Exponentially In Radius, r, Away From the Surface Of the Planet, Where the Mass Density Varies As ρ(r) = Po exp| | | |, For r2R- a) Using the Integral Form Of Gauss's 6. Law, [n.gda--4πGJsoh', And Spherical Coordinates (Specifically Using the...
Assume that a Spherical Planet Of Radius R, Has a Uniform Mass Density (Per Unit Volume) Distribution Throughout, Of Value Po. Also, Assume that There Is a Massive Dust Cloud In the Rest Of the Universe, Which Decays Exponentially In Radius, r, Away From the Surface Of the Planet, Where the Mass Density Varies As ρ(r) = Po exp| | | |, For r2R- a) Using the Integral Form Of Gauss's 6. Law, [n.gda--4πGJsoh', And Spherical Coordinates (Specifically Using the...
3. Tremaine et al. (2002) have shown that supermassive black holes in the nuclei of galaxies follow a relation between black hole mass, MB, and the velocity dispersion of the host galaxy bulge component, σ, such that log,o MBH8.0+40logo 200km/ The gravitational radius, Ra. (in a sense the "sphere of influence") of a black hole can be defined by the distance from the center at which the orbital speed of a star due to the black hole alone (i.e. neglecting...
4 A spherically symmetric charge distribution has the following radial dependence for the volume charge density ρ: 0 if r R where γ is a constant a) What units must the constant γ have? b) Find the total charge contained in the sphere of radius R centered at the origin c) Use the integral form of Gauss's law to determine the electric field in the region r R. (Hint: if the charge distribution is spherically symmetric, what can you say...
Only part f) please! 4 A spherically symmetric charge distribution has the following radial dependence for the volume charge density ρ ρ(r) If r > R where y is a constant a) What units must the constant y have? b) Find the total charge contained in the sphere of radius R centered at the origin c) Use the integral form of Gauss's law to determine the electric field in the region r < R. Hint: if the charge distribution is...
4. A spherically sym metric charge distribution has the following radial dependence for the volume charge density ρ 0 if r > R where γ is a constant a) What units must the constant y have? b) Find the total charge contained in the sphere of radius R centered at the origin. c) Use the integral form of Gauss's law to determine the electric field in the region r < R. (Hint: if the charge distribution is spherically symmetric, what...
Consider a cylindrical capacitor like that shown in Fig. 24.6. Let d = rb − ra be the spacing between the inner and outer conductors. (a) Let the radii of the two conductors be only slightly different, so that d << ra. Show that the result derived in Example 24.4 (Section 24.1) for the capacitance of a cylindrical capacitor then reduces to Eq. (24.2), the equation for the capacitance of a parallel-plate capacitor, with A being the surface area of...